The divergences, which are absent in asymptotic safety, are those we expect to appear if we only have an effective theory that involves an artificial UV cut-off \(\Lambda _{\rm UV}\) , characterising our ignorance of physics on small distances \(\ell < 1/\Lambda _{\rm UV}\) . An effective theory will break down as energies approach the cut-off scale and we will, therefore, encounter unphysical divergences.
In an asymptotically safe theory, such divergences should be absent since we have sent \(\Lambda _{\rm UV} \rightarrow \infty \) .
Indeed, the form of the flow Equation (REF ) assumes that the limit \(\Lambda _{\rm UV} \rightarrow \infty \)  has been taken and would take a modified form if an independent UV cut-off were introduced [1]}, [2]}.
Asymptotic safety requires that as we take some characteristic energy scale \(E \rightarrow \infty \)  observables (such as reaction rates) scale as
\(\mathcal {O} \sim E^{D} \,,\) 
